TSTP Solution File: NUM802^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM802^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:56:47 EDT 2022
% Result : Theorem 2.11s 2.30s
% Output : Proof 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 34 ( 9 unt; 5 typ; 1 def)
% Number of atoms : 60 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 94 ( 23 ~; 12 |; 0 &; 39 @)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 16 con; 0-2 aty)
% Number of variables : 12 ( 1 ^ 11 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_absval,type,
absval: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_c_2,type,
c_2: $i ).
thf(ty_c_less_,type,
c_less_: $i > $i > $o ).
thf(ty_c0,type,
c0: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( c_less_ @ ( absval @ X1 ) @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( c_less_ @ c_2 @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
~ ( X1 @ ( absval @ X2 ) )
=> ~ ( X1 @ c_2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( c_less_ @ ( absval @ eigen__1 ) @ c0 )
=> ( ( absval @ eigen__1 )
!= ( absval @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( c_less_ @ ( absval @ eigen__1 ) @ c0 )
=> ( ( absval @ eigen__1 )
!= ( absval @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i,X2: $i] :
( ( c_less_ @ X1 @ c0 )
=> ( X1
!= ( absval @ X2 ) ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( absval @ eigen__1 )
= ( absval @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( c_less_ @ ( absval @ eigen__1 ) @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: $i] :
~ ( c_less_ @ ( absval @ X1 ) @ c0 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
~ ( c_less_ @ ( absval @ X1 ) @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ( c_less_ @ X1 @ c0 )
=> ( X1
!= ( absval @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cBLEDSOE_FENG_8,conjecture,
sP7 ).
thf(h1,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[cBLEDSOE_FENG_8]) ).
thf(1,plain,
sP6,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| ~ sP8
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP10
| sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(6,plain,
( ~ sP9
| ~ sP10
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP5
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP5
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP7
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM802^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 08:13:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.11/2.30 % SZS status Theorem
% 2.11/2.30 % Mode: mode506
% 2.11/2.30 % Inferences: 96797
% 2.11/2.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------